All I meant was this seems like a tedious problem to work out in full, and once one does see the trick, working to the end and getting the correct answer becomes an exercise of a wholly different type. Its an exercise in tidy record keeping and double checking.

I once worked for a telecommunications lab, just as the parent company's IP networks were being grown. Losses due to "lost inventory" (physical assets unusable because key data about them was missing) were in the X-figure range. Now, you might think they would start doing some double checking of the data they were feeding the systems. But no, the answer was to promote exhortations "enter it once, enter it right!".

I wasn't impressed with that response, nor with the notion that "the trick" is all there is to this problem, if the expectation is that something like 4th graders are to work it all the way through and get the right answer.

By the way, the exhortation campaign and little effect on the bottom line.

My guess is that if only 18 out of 20 children failed to work this problem to a successful conclusion, it was not due to not "seeing the trick". My guess it it had to do with (lack of) tidy record keeping and double checking.